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model of investment.
The neoclassical model examines the benefits and costs
to firms of owning capital goods. The model shows how the level of invest-
ment—the addition to the stock of capital—is related to the marginal product of
capital, the interest rate, and the tax rules affecting firms.
To develop the model, imagine that there are two kinds of firms in the econ-
omy. Production firms produce goods and services using capital that they rent.
Rental firms make all the investments in the economy; they buy capital and rent
it out to the production firms. Most firms in the real world perform both func-
tions: they produce goods and services, and they invest in capital for future pro-
duction. We can simplify our analysis and clarify our thinking, however, if we
separate these two activities by imagining that they take place in different firms.
The Rental Price of Capital
Let’s first consider the typical production firm. As we discussed in Chapter 3, this
firm decides how much capital to rent by comparing the cost and benefit of each
unit of capital. The firm rents capital at a rental rate R and sells its output at a price
P; the real cost of a unit of capital to the production firm is R/P. The real benefit
of a unit of capital is the marginal product of capital MPK—the extra output pro-
duced with one more unit of capital. The marginal product of capital declines as the
amount of capital rises: the more capital the firm has, the less an additional unit of
capital will add to its output. Chapter 3 concluded that, to maximize profit, the firm
rents capital until the marginal product of capital falls to equal the real rental price.
Figure 18-2 shows the equilibrium in the rental market for capital. For the
reasons just discussed, the marginal product of capital determines the demand
curve. The demand curve slopes downward because the marginal product of cap-
ital is low when the level of capital is high. At any point in time, the amount of
capital in the economy is fixed, so the supply curve is vertical. The real rental
price of capital adjusts to equilibrate supply and demand.
To see what variables influence the equilibrium rental price, let’s consider a
particular production function. As we saw in Chapter 3, many economists con-
sider the Cobb–Douglas production function a good approximation of how the
actual economy turns capital and labor into goods and services. The
Cobb–Douglas production function is
Y
= AK
a
L
1
−
a
,
where Y is output, K is capital, L is labor, A is a parameter measuring the level
of technology, and
a
is a parameter between zero and one that measures capital’s
share of output. The marginal product of capital for the Cobb–Douglas produc-
tion function is
MPK
=
a
A(L/K )
1
−
a
.
C H A P T E R 1 8
Investment
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Because the real rental price R/P equals the marginal product of capital in equi-
librium, we can write
R/ P
=
a
A( L/ K )
1
−
a
.
This expression identifies the variables that determine the real rental price. It
shows the following:
■
The lower the stock of capital, the higher the real rental price of capital.
■
The greater the amount of labor employed, the higher the real rental
price of capital.
■
The better the technology, the higher the real rental price of capital.
Events that reduce the capital stock (an earthquake), or raise employment (an
expansion in aggregate demand), or improve the technology (a scientific discov-
ery) raise the equilibrium real rental price of capital.
The Cost of Capital
Next consider the rental firms. These firms, like car-rental companies, merely
buy capital goods and rent them out. Because our goal is to explain the invest-
ments made by the rental firms, we begin by considering the benefit and cost of
owning capital.
The benefit of owning capital is the revenue earned by renting it to the pro-
duction firms. The rental firm receives the real rental price of capital R/P for
each unit of capital it owns and rents out.
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